ci: Trigger doc release on stable release (#798)

## Summary

- The stable release pipeline was missing a doc release step, so the
changelog on the website was not updated after a stable release
- Added a `doc_release` job to `manual_release_stable.yaml` (same
pattern as `doc_release_post_publish` in `on_master.yaml`)
- The job runs after `changelog_update` and `pypi_publish`, using the
changelog commit ref to include the updated changelog

Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>

Author: vdusek

.github/workflows/manual_release_stable.yaml

@@ -95,6 +95,15 @@ jobs:
       - name: Publish package to PyPI
         uses: pypa/gh-action-pypi-publish@release/v1
 
+  doc_release:
+    name: Doc release
+    needs: [changelog_update, pypi_publish]
+    uses: ./.github/workflows/_release_docs.yaml
+    with:
+      # Use the ref from the changelog update to include the updated changelog.
+      ref: ${{ needs.changelog_update.outputs.changelog_commitish }}
+    secrets: inherit
+
   trigger_docker_build:
     name: Trigger Docker image build
     needs: [release_prepare, changelog_update]